Answers to Problems 2, 3 and 4. The reader should show how these results are obtained and generate the resulting closed-loop time domain plots.

Problem 2: Ziegler-Nichols PI: Gm = 1.97, Pm = 53, Wco = 0.33, Wpm = 0.16. Tyreus-Luyben: Gm = 3.09, Pm =102, Wco = 0.351, Wpm = 0.0746.

Problem 3: Gm = 2.00, Pm = 75.49, Wco = 0.366, Wpm = 0.161. Additional time delay = 8.18 minutes.

Problem 4: For l = 9.5, k_c = 1.315, Gm = 2.50. Increase l to obtain a Pm of at least 75°.